Comparison of interval methods for plotting algebraic curves

R Martin, H H Shou, I Voiculescu, A Bowyer, G J Wang

Research output: Contribution to journalArticle

59 Citations (Scopus)

Abstract

This paper compares the performance and efficiency of different function range interval methods for plotting f (x, y) = 0 on a rectangular region based on a subdivision scheme, where f (x, y) is a polynomial. The solution of this problem has many applications in CAGD. The methods considered are interval arithmetic methods (using the power basis, Bernstein basis, Homer form and centred form), an affine arithmetic method, a Bernstein coefficient method, Taubin's method, Rivlin's method, Gopalsamy's method, and related methods which also take into account derivative information. Our experimental results show that the affine arithmetic method, interval arithmetic using the centred form, the Bernstein coefficient method, Taubin's method, Rivlin's method, and their related derivative methods have similar performance, and generally they are more accurate and efficient than Gopalsamy's method and interval arithmetic using the power basis, the Bernstein basis, and Horner form methods. (C) 2002 Elsevier Science B.V. All rights reserved.
Original languageEnglish
Pages (from-to)553-587
Number of pages35
JournalComputer Aided Geometric Design
Volume19
Issue number7
Publication statusPublished - 2002

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Interval Methods
Algebraic curve
Derivatives
Polynomials
Interval Arithmetic
Bernstein Basis
Derivative
Subdivision Scheme
Coefficient

Cite this

Martin, R., Shou, H. H., Voiculescu, I., Bowyer, A., & Wang, G. J. (2002). Comparison of interval methods for plotting algebraic curves. Computer Aided Geometric Design, 19(7), 553-587.

Comparison of interval methods for plotting algebraic curves. / Martin, R; Shou, H H; Voiculescu, I; Bowyer, A; Wang, G J.

In: Computer Aided Geometric Design, Vol. 19, No. 7, 2002, p. 553-587.

Research output: Contribution to journalArticle

Martin, R, Shou, HH, Voiculescu, I, Bowyer, A & Wang, GJ 2002, 'Comparison of interval methods for plotting algebraic curves', Computer Aided Geometric Design, vol. 19, no. 7, pp. 553-587.
Martin R, Shou HH, Voiculescu I, Bowyer A, Wang GJ. Comparison of interval methods for plotting algebraic curves. Computer Aided Geometric Design. 2002;19(7):553-587.
Martin, R ; Shou, H H ; Voiculescu, I ; Bowyer, A ; Wang, G J. / Comparison of interval methods for plotting algebraic curves. In: Computer Aided Geometric Design. 2002 ; Vol. 19, No. 7. pp. 553-587.
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